{
  "annotation_id": "8112314c-697c-4d74-94c9-95d05eafe927",
  "date_created": "2026-03-02T18:02:09.928000Z",
  "date_modified": "2026-03-02T18:02:09.928000Z",
  "file_hash": "2e92ee80ac61ab6f0893ef497cf858ddacfa714d034d6de1947570590d3666af",
  "private": false,
  "record": {
    "abstract": "A complete set of N+1 mutually unbiased bases (MUBs) exists in Hilbert spaces\nof dimension N = p^k, where p is a prime number. They mesh naturally with\nfinite affine planes of order N, that exist when N = p^k. The existence of MUBs\nfor other values of N is an open question, and the same is true for finite\naffine planes. I explore the question whether the existence of complete sets of\nMUBs is directly related to the existence of finite affine planes. Both\nquestions can be shown to be geometrical questions about a convex polytope, but\nnot in any obvious way the same question.",
    "arxiv_id": "quant-ph/0406174",
    "authors": [
      "Ingemar Bengtsson"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1063/1.1874558",
    "title": "MUBs, polytopes, and finite geometries",
    "url": "https://arxiv.org/abs/quant-ph/0406174"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "350c465a-513b-464e-82d0-6931420607c2",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}